As expected, the RAS iterative scheme shows excellent scalability for the chosen datasets, and the overall time to compute the MFA in parallel was reduced at a nearly ideal rate up to \(10^3\)  MPI tasks as \(\mathcal {N}\)  increases, while ensuring \(C^{p-1}\)  continuity in the subdomain interfaces. It is important to note that the dominant computational time is driven by the decoupled LSQ solution computation and decoding operations, which are embarassingly parallel as the size of the subdomains (determined by number of knot spans) decreases in direct proportion to the tasks. Given that the scalability of the linear algebraic LSQ solvers [1]}, [2]} and Sparse Matrix Vector (SpMV) products used in the decode tasks are well understood, the bottlenecks potentially occur only from the nearest neighbor communication for constraint data exchanges, which remain relatively small in magnitude up to 32K processes tested in the 3D experiments. The overall strong scaling efficiency remains around 50% for both overlapping and non-overlapping 2D problem cases at 16,384 tasks. However, the added setup cost and less than ideally scaling nearest neighbor communications reduce the 3D problem efficiency for the overlapping subdomain cases to 25% at 32,768 tasks from 70% in the nonoverlapping cases.
